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We consider a chain of regularly-spaced spherical metallic nanoparticles,where each particle supports three degenerate localized surface plasmons. Dueto the dipolar interaction between the nanoparticles, the localized plasmonscouple to form extended collective modes. Using an open quantum system approachin which the collective plasmons are interacting with vacuum electromagneticmodes and which, importantly, readily incorporates retardation via thelight-matter coupling, we analytically evaluate the resulting radiativefrequency shifts of the plasmonic bandstructure. For subwavelength-sizednanoparticles, our analytical treatment provides an excellent quantitativeagreement with the results stemming from laborious numerical calculations basedon fully-retarded solutions to Maxwell's equations. Indeed, the explicitexpressions for the plasmonic spectrum which we provide showcase how includingretardation gives rise to a logarithmic singularity in the bandstructure oftransverse-polarized plasmons. We further study the impact of retardationeffects on the propagation of plasmonic excitations along the chain. While forthe longitudinal modes, retardation has a negligible effect, we find that theretarded dipolar interaction can significantly modify the plasmon propagationin the case of transverse-polarized modes. Moreover, our results elucidate theanalogy between radiative effects in nanoplasmonic systems and the cooperativeLamb shift in atomic physics.

Retardation effects on the dispersion and propagation of plasmons in metallic nanoparticle chains